A semilinear partial differential equation induced by Hermitian Yang-Mills metrics

TL;DR

This paper investigates a class of semilinear PDEs arising from Hermitian Yang-Mills metrics, focusing on radial symmetry of solutions in 2 and existence of boundary value solutions in bounded domains.

Contribution

It establishes the radial symmetry of global solutions and proves the existence of solutions with boundary conditions for these PDEs.

Findings

Radial symmetry of 2 solutions in 2

Existence of 2,lpha solutions in bounded domains

Analysis of limiting behavior of Hermitian Yang-Mills metrics

Abstract

This paper will discuss a class of semilinear partial differential equations induced by studying the limiting behaviour of Hermitian Yang-Mills metrics. We will study the radial symmetry of the $C^{2}$ global solution of this equation in $\mathbb{R}^{2}$ and the existence of $C^{2,\alpha}$ solution of the Dirichlet boundary value problem in any bounded domain.